Open AccessOn Independent Transversal Dominating Sets in Graphs
Author(s) -
Daven Sapitanan Sevilleno,
Ferdinand P. Jamil
Publication year - 2021
Publication title -
european journal of pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.245
H-Index - 5
ISSN - 1307-5543
DOI - 10.29020/nybg.ejpam.v14i1.3904
Subject(s) - transversal (combinatorics) , mathematics , dominating set , combinatorics , maximal independent set , independent set , cardinality (data modeling) , graph , discrete mathematics , set (abstract data type) , domination analysis , chordal graph , 1 planar graph , vertex (graph theory) , mathematical analysis , computer science , data mining , programming language
A set S ⊆ V (G) is an independent transversal dominating set of a graph G if S is a dominating set of G and intersects every maximum independent set of G. An independent transversal dominating set which is a total dominating set is an independent transversal total dominating set. The minimum cardinality γit(G) (resp. γitt(G)) of an independent transversal dominating set (resp. independent transversal total dominating set) of G is the independent transversal domination number (resp. independent transversal total domination number) of G. In this paper, we show that for every positive integers a and b with 5 ≤ a ≤ b ≤ 2a − 2, there exists a connected graph G for which γit(G) = a and γitt(G) = b. We also study these two concepts in graphs which are the join, corona or composition of graphs.